Quantized circular motion of a trapped Bose-Einstein condensate: Coherent rotation and vortices

We study the creation of vortex states in a trapped Bose-Einstein condensate by a rotating force. For a harmonic trapping potential the,rotating force induces only a circular motion of the whole condensate around the trap center which does not depend on the interatomic interaction. For the creation of a pure vortex state it is necessary to confine the atoms in an anharmonic trapping potential. The efficiency of the creation can be greatly enhanced by a sinusoidal variation of the force's angular velocity. We present analytical and numerical calculations for the case of a quartic trapping potential. The physical mechanism behind the requirement of an anharmonic trapping potential for the creation of pure vortex states is explained.